The authors calculated the effect size for treatments recommended for the pediatric population in the new Guidelines for the Management of Postoperative Nausea and Vomiting that should be implemented with the help of a new risk scale developed for children.

Six single-drug therapies and five combination treatments were subjected to a Bayesian analysis, with respect to the outcome reported, in a sequence that parallels their dates of publication. Based on the Bayes theorem, a posterior probability was calculated after inclusion of the data from the successive studies, to update a prior probability existing before inclusion of that study. The posterior for the preceding group of trials served as the prior for the subsequent trial. The final odds ratio with its 95% credibility interval compared with placebo is considered as the results for that treatment, and was transformed into a relative risk whose 95% credibility interval allows the calculation of a most pessimistic and a most optimistic incidence of postoperative vomiting.

The most pessimistic expectations with the 5-hydroxytryptamine receptor antagonists and dexamethasone result in a 50-60% relative risk reduction. The results with droperidol offer a decrease of only approximately 40%. With the combinations of a 5-hydroxytryptamine receptor antagonist and dexamethasone, a relative risk reduction of approximately 80% is expected.

The authors' tables list the expected incidence of postoperative vomiting with each treatment for each risk category, and the expected relative risks that can be used with baseline risk values from any source.

RECENTLY, a new set of Guidelines for the Management of Postoperative Nausea and Vomiting has been published.1These guidelines contain extensive recommendations for treatment in children and should be implemented with the help of a new risk scale developed for children.2Despite the description of several pharmacologic therapies using single drugs or combinations, no precise expected size of treatment effect is given in these guidelines.

The aim of this article is to calculate the various effect sizes for each treatment recommended in the pediatric population, expressed as a relative risk (RR) that can be obtained using the treatments suggested in the new guidelines. Once these RRs are obtained, the risk of postoperative vomiting can be computed for each of the risk categories described in the new pediatric risk scale.

## Materials and Methods

This article considers the efficacy of six single-drug therapies and five combination treatments. The single drugs are ondansetron, tropisetron, granisetron, dolasetron, dexamethasone, and droperidol. The combinations for which there is an existing pediatric literature are ondansetron plus dexamethasone, ondansetron plus droperidol, tropisetron plus dexamethasone, dolasetron plus dexamethasone, and granisetron plus dexamethasone. All of these treatments were administered by the intravenous route during surgery, with the exception of two ondansetron, one ondansetron plus dexamethasone, one granisetron, and one dolasetron trial, where they were given orally before surgery.

### Search Strategy

We looked for controlled trials, including only children, in the postoperative setting, and in which the incidence of postoperative vomiting or nausea was one of the endpoints. The comparator had to be a placebo for the single-drug treatments; for the combination treatments, one of the drugs in the combination, or placebo, had to serve as the comparator. We included only treatments listed in the new Guidelines for the Management of Postoperative Nausea and Vomiting.1

For ondansetron, we searched PubMed with the search criteria *ondansetron* and *postoperative* , with the limits human clinical trials and children aged 0–18 yr. This search produced a list of 174 articles. These articles were searched manually and produced 14 trials3–16comparing ondansetron with a placebo. Five trials compared ondansetron plus dexamethasone with ondansetron14,17or dexamethasone18–20alone, and in one study,14a placebo was also used as a comparator. The remainder comprised 59 trials in adults, 43 trials that were not adequately controlled, 47 trials in which postoperative vomiting or nausea was not an endpoint or that were not in the postoperative setting, or did not concern ondansetron at all. Seven articles were reviews or meta-analyses.

For tropisetron, we searched PubMed with the search criterion *tropisetron* , with human clinical trials and children aged 0–18 yr used as limits. The search produced 45 trials. Five trials21–25using tropisetron alone and 1 trial26using tropisetron plus dexamethasone were found in this list. Twenty-five trials were in the setting of chemotherapy, 2 trials were not placebo controlled, 7 trials were in fact in adults, and in 5 trials postoperative nausea or vomiting was not an endpoint or they were not in the postoperative setting. Using the key words *postoperative* and *tropisetron* produced 1 trial27using tropisetron plus dexamethasone that was not in the previous list.

For dolasetron, we searched PubMed with the search criterion *dolasetron* , with human clinical trials and children aged 0–18 yr used as limits. The search produced 22 trials. Two trials16,28using dolasetron alone and a single trial20using dolasetron plus dexamethasone were found in this list. Two trials were in the setting of chemotherapy, 2 trials were not placebo controlled, 8 trials were in fact in adults, and in 7 trials postoperative nausea or vomiting was not an endpoint or they were not in the postoperative setting. Using the key words *postoperative* and *dolasetron* did not allow us to find other trials.

For granisetron, we searched PubMed with the search criterion *granisetron* , with human clinical trials and children aged 0–18 yr used as limits. The search produced 79 trials. However, it must be noted that serious doubts29have been expressed about the validity of the studies from Fujii *et al.* ; they were therefore excluded from our analysis, and the list was reduced to 57 after exclusion of the trials by Fujii *et al.* , including 4 trials30–33in children using granisetron alone and 2 trials34,35with a combination of granisetron plus dexamethasone. Three trials36–38using granisetron alone and 1 trial38using granisetron plus dexamethasone were found in this list and are included in our analysis. Forty-one trials were in the setting of chemotherapy, 3 trials were not placebo controlled, 3 trials were in fact in adults, and in 7 trials postoperative nausea or vomiting was not an endpoint or they were not in the postoperative setting. Using the key words *postoperative* and *granisetron* did not allow us to find other trials.

For dexamethasone, we searched PubMed for the simultaneous key words *dexamethasone* , *children* , and *postoperative* . This produced a list of 68 articles. One trial was in adults, 3 trials were not placebo controlled, in 49 articles postoperative vomiting was not an endpoint or they were general review articles or were not in the postoperative setting, and 1 article was a meta-analysis.39Three trials concerned combination treatments (ondansetron plus dexamethasone). Twelve randomized controlled trials40–51were included in our analysis. Searching for key words *tonsillectomy* and *dexamethasone* , and *strabismus* and *dexamethasone* did not produce other trials.

For droperidol, we searched PubMed for the key words *droperidol* , *postoperative* , and *children* , with the limits clinical trials and age 0–18 yr. This search produced 66 articles. Only 3 trials13,52,53were included in our analysis; it must be noted that only studies using a low dose of 5–25 μg/kg droperidol are included, as higher doses are not recommended in the new guidelines because of the higher rate of extrapyramidal syndrome reported in children. One of these trials also compared ondansetron plus droperidol with a placebo.13

Twelve trials used a high dose (≥ 50 μg/kg) of droperidol, 20 trials were not properly controlled by our definition, 2 articles were reviews, and in 29 articles postoperative vomiting was not an endpoint or they were not in the postoperative setting or were completely unrelated to the prevention of postoperative vomiting by droperidol.

We cross-checked the lists of trials that we obtained by this search strategy with the trials included in the Cochrane review,54the latest meta-analysis on ondansetron,55dexamethasone,39and droperidol56in children, and we could identify one more trial regarding dexamethasone.57The 2 additional trials found in the meta-analysis of Henzi *et al.* 56were not selected because of the use of a high dose (50 and 75 μg/kg) of droperidol.

All of the trials were prospective randomized controlled trials, with one exception,27which was a retrospective study with matching controls.

For all drugs, different doses of the same drug were used by different authors. For ondansetron (0.1–0.3 mg/kg), tropisetron (0.1–0.2 mg/kg), and droperidol (5–25 μg/kg), the difference between the highest and lowest dose was not excessively different. For all of these drugs, the obvious decision was to make a single analysis with all doses grouped together. With granisetron, the guidelines1recommend only 40 μg/kg, which was the dose selected for our analysis. But for dexamethasone, the doses ranged from 0.050 to 1.0 mg/kg, a 20-fold difference. However, 3 trials included a dose-ranging study; ranges from 0.050 to 0.250 mg/kg,420.250 to 1.0 mg/kg,43and 0.0625 to 1.0 mg/kg58were studied, and there was no indication of a dose response. Therefore, we decided to make a single analysis with all doses grouped together.

### Statistical Analysis

We subjected the studies to a Bayesian analysis, with respect to the outcome reported, in a sequence that paralleled their dates of publication. Because many readers are probably unfamiliar with the methodology of Bayesian analysis, we provide an explanation of the method, kept as practical as possible, in appendix 1.

Based on the Bayes theorem, a posterior probability was calculated after inclusion of the data from the successive studies, to update a prior probability existing before inclusion of that study. For the first computation, for inclusion of the data from the first study, we used a noninformative prior probability, with a log odds ratio (OR) mean equal to 0 and an SD of the distribution of ORs equal to 10. This gives a flat distribution of the probabilities at this point and gives an equal probability to either treatment being superior to the other, given the absence of previous data, and starts the following comparisons from a neutral point of view. It is a 50/50 situation (log OR = 0 gives an OR = 1, and the SD of 10 means that 95% of the ORs values are between 0.0094 and 406.4207) and allows starting from a neutral standpoint. This is also called an uninformative prior. Thereafter, the posterior for the preceding group of trials served as the prior for the subsequent trial.

The mean log OR and the SD of the log ORs obtained at the end of the analysis were transformed to an OR and 95% credibility interval. These ORs were transformed to RRs by using the method of Zhang and Yu.59

The baseline risks (BLRs) of 70, 55, 30, and 10% described for the various risk categories on the pediatric risk scale2were updated using the computed RR in the formula (BLR − (BLR × (1 − RR))).

Two RRs were used that formed the upper and lower border of the 95% credibility interval. This resulted in a most optimistic value (using the lower border of the interval) and a most pessimistic value (using the upper border of the interval). These represent the lowest and highest risk values that can be expected with a 95% probability when treating a child from a given BLR category.

For each single-drug treatment and for the ondansetron plus droperidol and the granisetron plus dexamethasone combinations tested against a placebo, the procedure described was straightforward.

For the combination treatments that were not tested against a placebo (ondansetron plus dexamethasone, tropisetron plus dexamethasone, and dolasetron plus dexamethasone), an RR and 95% credible interval was computed against the single drug tested, using the same methodology as described for a single-drug treatment. Thereafter, an indirect comparison method, as suggested by Bucher *et al.* ,60was used to extrapolate the RR of the combination against a placebo; this allowed calculation of a posttreatment risk using the same method as for the single-drug treatments.

The equations used for all calculations are given in appendixes 1 and 2.

All computations were made using the software program Lotus 1-2-3 97 Edition (IBM, Armonk, NY).

## Results

The endpoints used in all of the included trials are given in table 1. The wording used is taken verbatim from the original article and is not our interpretation. The third column reports emetic symptoms that were explicitly not considered as an endpoint; the word *no* means simply that no exclusion is explicitly reported by the authors in the methodology section. The last column reports specific exclusion or inclusion criteria.

Vomiting is almost uniformly reported, with retching specifically included in more than half of the trials; however, in 6 trials, retching is explicitly not counted as an endpoint. Many studies also report some sort of children exclusion usually connected with recent treatment or occurrence of some sort of emetic symptom. Six trials report specifically excluding children with motion sickness and/or a history of postoperative vomiting.

The analysis of all the included trials are given in tables 2–13, including year of publication, the doses used, the type of surgery, the age of the children included, the number of children included in each group, and the number of children presenting the postoperative endpoint (called postoperative vomiting [POV] in the tables) in the group. The final column gives the mean ORs and their 95% credibility intervals resulting from the calculations after inclusion of each trial in the analysis.

The last OR is considered as the result obtained with the treatment in question. Tables 2 and 3show the analysis for the trials with ondansetron compared with placebo; they list all of the intermediate logarithmic results to highlight the details of the methodology used.

The final ORs for all the treatments, and their transformation into RRs with their 95% credibility intervals, are given in table 14. Using the boundaries for these credibility intervals, the highest and lowest incidences expected with each treatment are given in table 15.

It seems that globally, the combination treatments result in lower RRs, and thus lower expected risks, than the single-drug treatments. When one considers the most pessimistic expectations, the best single-drug prophylaxis with the 5-hydroxytryptamine receptor antagonists and dexamethasone result in a 50–60% RR reduction. The results with droperidol offer a decrease of only approximately 40%.

It is also clear that the smallest credibility intervals, resulting in the smallest difference between the most optimistic and pessimistic stands, are obtained with ondansetron and dexamethasone; this can be attributed to the fact that these treatments were studied in the greatest number of trials, and the effect is thus known with the best precision.

With the combinations of a 5-hydroxytryptamine receptor antagonist and dexamethasone, one can expect an RR reduction of approximately 80%.

### Sensitivity Analysis

However, in all of the published trials including only children, none concluded with a superiority of the placebo or the single-drug comparator. The study drug was statistically significantly better in all but 6 trials, which showed a strong but nonsignificant superiority of the study drug. This raises the possibility of a publication bias.

Using our method of calculation, a potential bias can be taken into account by changing the initial value of the prior, to take a more skeptic stand at the beginning of the analysis ( appendix 3). In our case, the obvious choice seems to be to take as the initial probability the values reported in the trials with adult patients,54,61reporting an RR reduction of approximately half of the values we just reported.

Table 16reports the values computed at the end of our reanalysis for the drug treatments for which we were able to find this appropriate prior probability. The results obtained for ondansetron and dexamethasone are nearly identical to those obtained with the noninformative prior, showing that with sufficient data available, the end results remains strongly in favor of this important effect. The other treatments, however, were unable to overcome this computational handicap. The expected incidences of postoperative vomiting using these skeptical priors are listed in table 17.

## Discussion

Two key elements can be concluded from our results. The first one is that the RR reduction measured in children is approximately double that reported in adult patients, with all categories of drugs. This could indeed seem to be an unlikely increase in efficiency, and indeed the responsibility of a publication bias cannot be totally excluded; nevertheless, even after correction for this possibility, the magnitude of the therapeutic effect size was almost unchanged for ondansetron and dexamethasone. The second point is that with a treatment combining a 5-hydroxytryptamine receptor antagonist and dexamethasone or droperidol, an RR reduction of approximately 80% can be expected.

Although there is some overlap between the 95% credibility intervals for some single-drug and some combination treatments, overlap occurs essentially between treatments that have the widest 95% credibility intervals; these are the treatments with the smallest number of trials and patients. For the treatments with smaller 95% credibility intervals, ondansetron, tropisetron, and dexamethasone, there is no overlap when compared with ondansetron plus dexamethasone or tropisetron plus dexamethasone.

As stated before, the calculations for all the single-drug treatments and for the ondansetron plus droperidol combination are straightforward because they were compared with placebo. The other combinations were compared with single-drug treatments, and therefore, to be able to make a statement about their effect compared with placebo, we had to resort to the extra step of making an indirect comparison.

Indirect comparisons usually, but not always, agree with the results of head-to-head randomized trials. The only requirement is that the magnitude of the treatment effect is constant across differences in the populations' baseline characteristics. When there is no or insufficient direct evidence from randomized trials, the adjusted indirect comparison may provide useful or supplementary information on the relative efficacy of competing interventions.62,63The validity of the adjusted indirect comparisons depends on the internal validity and similarity of the included trials. In the case of ondansetron plus dexamethasone, we have a single study against placebo. The 95% credibility intervals for this study did overlap with the results obtained from indirect comparison, but it must nevertheless be noted that the 95% credibility interval for this study is so large that the probability of overlapping is great, in the absence of an enormous difference that would probably be generated from large differences in the studied populations.

From a practical point of view, the results in table 14can serve as a guide for performing a cost-effectiveness evaluation. The prices of all the drugs and the financing from the various health insurance systems vary greatly across the world. For example, postoperative vomiting has been reported as a main reason for unplanned overnight hospital admission.64A cost effectiveness calculation taking into account the local expenses related to the drugs and the eventual hospital admission can be balanced for each risk category described on the pediatric risk scale; it could seem that for certain low-risk patients, only single-drug prophylaxis is cost-effective.

Our final results expressed in absolute percentage of vomiting depend, of course, of the incidences ascribed to each category of the pediatric risk scale, which is not without weaknesses. Some questioning about this scale was already published, because age older than 3 yr and surgery for more than 30 min (two of the four risk markers) were not found to be markers of increased risk in a recent study.58However, the ORs and RRs that we computed are independent of this risk scale and can always be used with different BLR values. One can even use values from his or her own practice and the results from table 14to calculate the expected incidence with the various treatments.

Another problem arising from all of these studies in children is the variability of the endpoint (the description of the actual emetic events counted), as well as of the inclusion and exclusion criteria (table 1). This probably results in underreporting of emetic events because of the exclusion of retching in certain trials and the absence of counting nausea in most studies, even if this could have been reported by the older children. The effect of excluding the children with a history of postoperative vomiting or motion sickness or a recent emetic event could have as a consequence exclusion of the children with the highest risk from many trials, a consequence whose influence on our results can only be speculative.

This underreporting could also partly account for the increased efficiency of the treatments in children, because in adults a large portion of postoperative nausea and vomiting is in fact nausea. In the study of Apfel *et al.* ,61which served as our reference in adults for ondansetron, dexamethasone, and droperidol, all emetic symptoms (vomiting, retching, and nausea) were counted as an event. This could be the case, because it seems that when taking the results from table 1in the Cochrane review,54the RR after treatment was lower for vomiting than for nausea, and the results for ondansetron, dexamethasone, and droperidol are similar to those obtained in our current analysis (table 18).

As a whole, it seems that the expected incidences values in table 15are usually very close to measured incidences in the trials, but that sometimes (as for the tropisetron65and tropisetron plus dexamethasone treatments) they seem to predict lower incidences that those measured. But it is also difficult to verify the accuracy of predictions with data that were in fact used to produce the statistical model, with the exception of the studies from Kim *et al.* 58and Gross *et al.* 65On the other hand, the ORs and RRs in table 14could represent accurately the effectiveness of the treatments, but the BLRs in some studies were not similar to those reported in the pediatric risk score.2

#### Appendix 1

The Bayesian paradigm considers that the role of data is to update our knowledge of a question under scrutiny that is considered as a parameter of interest in a statistical model.

In our case, the parameter of interest is the odds ratio.

Therefore, a fundamental feature of Bayesian analysis is the incorporation of prior information about the parameter of interest. The Bayes theorem gives a simple and uncontroversial result in probability theory, relating probabilities of events before (the “prior” in Bayesian parlance) and after an experiment (the “posterior” in Bayesian parlance).

Therefore, the prior information, expressed as a probability distribution for the parameter of interest, represents what is known before the data are taken into account; the data are expressed as a probability distribution known as the likelihood function, which demonstrates the degree of support from the data for the various possible values of the parameter of interest. The likelihood function is integrated with the prior to produce the posterior distribution, which represents our updated knowledge of the parameter of interest, given the data.

Following the work of Spiegelhalter *et al.* ,66we use normal distributions to summarize the information about the odds ratios on the natural log scale. The Bayesian inference supports direct statements about the probability of the magnitude of an effect, and therefore the 95% credibility interval means exactly what it is supposed to, *i.e.* , that there is a 95% probability that the real value of the odds ratio lies between the two borders.

Another advantage offered from our calculation methodology is the ease in updating the current data. Additional trials can be added easily to the analysis to provide a new evaluation of the expected efficacy.

##### Computational Methodology

This appendix highlights the methodology used to compute the odds ratio and the relative risk, derived from the Bayes theorem, representing the effectiveness of a treatment.

The equations are not presented in a general mathematical form, but show the particularities and use a naming convention adapted to the situation of analyzing trials expressed as a number of events in a “treated group” and a “control group.”

Once a first logarithm of posterior odds ratio, with its SD, is obtained as explained below, these values serve as prior for the calculation after inclusion of the data of the next study (see table 3for application of the method). This mechanism is repeated until inclusion of all trials.

This methodology is best understood by integrating these explanations with the intermediate results listed in table 3as an example.

E

^{T}= number of patients with event in treated groupnoE

^{T}= number of patients without event in treated groupn

^{T}= number of patients in treated groupE

^{C}= number of patients with event in control groupnoE

^{C}= number of patients without event in control groupn

^{C}= number of patients in control groupOR

^{d}= odds ratio from the datavar(OR

^{d}) = variance of the distribution of odds ratiosSD(OR

^{d}) = SD of the distribution of odds ratioslog OR

^{d}= natural logarithm of odds ratio from the data

##### Computation of the Natural Logarithm of the Posterior Odds Ratio

logOR

^{p}= natural logarithm of the prior odds ratioSD(logOR

^{p}) = SD of the distribution of the natural logarithm of prior odds ratiosvar(logOR

^{p}) = variance of the distribution of the natural logarithm of prior odds ratiosvar(logOR

^{p}) = (SD(logOR^{p}))^{2}logOR = natural logarithm of posterior odds ratio

SD(logOR) = SD of the distribution of the natural logarithm of the posterior odds ratios

##### Transform to a Posterior Odds Ratio

##### 95% Credibility Interval of Odds Ratio

##### Transform Odds Ratios to Relative Risks (RRs)

#### Appendix 2

##### Indirect Comparison

Relative risk of single-drug treatment

*versus*placebo: RR^{S/PBO}Relative risk of combination

*versus*single-drug treatment: RR^{C/S}Relative risk of combination treatment

*versus*placebo: RR^{C/PBO}

##### Calculation of the 95% Credibility Interval

The variance of the natural logarithm of a relative risk is calculated as

where ub = upper border of the 95% credibility interval and lb = lower border of the 95% credibility interval.

This allows the calculation of

by using the upper and lower borders of the 95% credibility intervals that can be found in table 14.

From (1)and (2),

From (3), the 95% credibility interval for RR^{C/PBO}can be calculated as

#### Appendix 3

In the current situation, an interesting feature of the Bayesian techniques can be use to tackle the two obvious problems that appear at the end of our initial analysis. The first is the size of the risk reduction, which is approximately double what is reported in adult patients. The second problem is the possibility of facing a publication bias.

Skepticism about large treatment effects can be formally expressed and used in interpretation of results that cause surprise. Rarely in medicine is there a situation where we know absolutely nothing about the probability of a treatment to succeed and are therefore only able to use a noninformative prior.

For the current analysis, we have a vast amount of data in adult patients from which we can make an initial informed guess of the likely therapeutic effect.

This is done by computing a prior probability (“prior”) than can serve as the initial value at the start of the Bayesian analysis; this makes it much harder to find a large effect of the treatment. The computational mechanism of our Bayesian meta-analysis is influenced by the size of the SD of the distribution of the natural logarithm of the odds ratios: the smaller the size, the bigger the skepticism expressed.

This is the formal way of introducing a skeptical view on the initial (and maybe too good) results. If, despite this “handicap,” the end results of our initial analysis can be (or can almost be) repeated, this is a strong indication that indeed, the results can be as extreme as those we obtained initially.

Starting a Bayesian analysis with different priors is called a sensitivity analysis, and shows how a result can be influenced by an initial belief before even beginning a study. Of course, with sufficiently strong data, the clinical conclusion should be the same with any reasonable initial prior probability.

The following section shows how to compute a prior based on values of maximal expected risk decrease and increase that are taken from the existing literature (in our case, the data on adult patients).

The results from this analysis and the data on which we have performed these computations are shown in table 16.

##### Computation of the Mean and SD for a 95% Confidence Interval of the Associated Normal Distribution with All Possible Values of the Odds Compatible with One's Belief

A = maximal expected decrease in odds ratio (if 15%, use 0.85)

B = maximal expected increase in odds ratio (if 15%, use 1.15)

Log(A) = natural logarithm of A

Log(B) = natural logarithm of B

log OR = natural logarithm of mean odds ratio

SD(log OR) = SD of the distribution of the natural logarithm of the odds ratios

These values are used as the initial prior probabilities to begin the Bayesian meta-analysis.

In table 16, the maximal expected decrease in odds ratio corresponds to the lower bound of the 95% confidence interval for the odds ratio computed from the data in references 54and 61. It was also hypothesized that there was no increase in risk to be expected with the administration of the treatment.

## References

*versus*dexamethasone plus low-dose ondansetron. Paediatr Anaesth 2001; 11:591–5

*versus*late intraoperative administration of tropisetron for the prevention of nausea and vomiting in children undergoing tonsillectomy and/or adenoidectomy. Paediatr Anaesth 2006; 16:444–50